Question

Expected return and standard deviation.

Use the following information to answer the questions.

State of   Economy		Probability of State		Return on Asset A in State		Return on Asset B in State		Return on Asset C in State
Boom		0.34		0.02		0.22		0.35
Normal		0.52		0.02		0.09		0.23
Recession		0.14		0.02		−0.02		−0.21

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.

Answer 1

Solution:

a. The expected return for each asset is calculated by multiplying the probabilities of return with the return on each asset.

= 0.34*0.02 + 0.52*0.02 + 0.14*0.02

= 0.02 or 2%

= 0.34*0.22 + 0.52*0.09 + 0.14*(-0.02)

= 0.1188 or 11.88%

= 0.34*0.35 + 0.52*0.23 + 0.14*(-0.21)

= 0.2092 or 20.92%

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b. The variance for each asset is calculated using the following formula

= 0.34*(0.02 - 0.02)^2 + 0.52*(0.02 - 0.02)^2 + 0.14*(0.02 - 0.02)^2

= 0

= 0.34*(0.22 - 0.1188)^2 + 0.52*(0.09 - 0.1188)^2 + 0.14*(-0.02 - 0.1188)^2

= 0.00661056 or 66.1056 (%)^2

= 0.34*(0.35 - 0.2092)^2 + 0.52*(0.23 - 0.2092)^2 + 0.14*(-0.21 - 0.2092)^2

= 0.003156736 or 315.6736 (%)^2

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c. The standard deviation for each asset is the square root of the variance

0 = 0

66.1056 = 8.13%

315.6736 = 17.77%